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Existence of limiting boundary and initial values of weak solutions of parabolic equation. (Russian)
Authors: Zhitarashu N. V.
Abstract
Theorems on existence of limit values of the derivatives in the normal direction $\nu$ to $S$, $D^{k-1}_{\nu}u$ on $S$ and the limit values when $t=0$ of derivatives $D^{\lambda -1}_t u$ in the Sobolev--Slobodetskii spaces are proven for weak solutions (distributions) $u(x,t)$ of the linear parabolic equations in the boundet cylindrical domain $\Omega = G\times (0,T)$, $S=\partial G\times (0,t)$.Universitatea de Stat din Moldova
str. Mateevici 60, MD-2009 Chişinău, Moldova
str. Mateevici 60, MD-2009 Chişinău, Moldova
Contents
- Topological classification of quadratic systems with a unique finite second order singularity with two zero eigenvalues. (English)
- Lyapunov stability and attraction of rest points of dynamical systems. (Russian)
- Connectedness of the Levinson center of a compact dissipative dynamical system without uniqueness. (Russian)
- Analytic continuation with respect to a parameter in the neighbourhood of zero of Green's function of basic external boundary value problems for the Helmholtz equation. (Russian)
- On absence of eigenvalues of singular, not selfadjoint differential operators. (Russian)
- Affine-invariant conditions for determining the number and multiplicity of singular points of quadratic differential systems. (English)
- Analysis of the condition ${\germ A}(k)$ for four-dimensional systems of differential equations. (Russian)
- Existence of limiting boundary and initial values of weak solutions of parabolic equation. (Russian)
- $L\sb 2$-estimates of solutions of the singular hyperbolic equations. (English)
- Energetic type estimates for singular hyperbolic equations of high order. (English)
- On sufficient conditions of the center for a cubic system of differential equations. (Russian)
- Concordant solutions of multidimensional differential equations. (English)
- Linear particular integrals and the problem of the center. (Russian)
- On algebraic differential equations with an integrating factor of Darboux type. (Russian)
